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Question
A number is increased by 25% and then decreased by 20%. Find the percentage change in that number
Solution
Method 1:
Let the number be x.
First it is increased by 25%
∴ It becomes `x + 25/100 xx x = 125/100`
Secondary it is decreased by 20%
`125/100x - 20/100 xx 125/100x = 125/100x xx 80/100` = x
Now we get back x, therefore there is no change.
Hence percentage change in that number is 0%
Method 2:
To understand, let us assume that number is 100
So, first when we increase by 25%, we get
`100 + 25/100 xx 100` = 100 + 25 = 125
Now this 125 is decreased by 20%, we get
`125 - 20/100 xx 125` = 125 – 25 = 100
∴ We get back 100 ⇒ No change
Hence percentage change in that number is 0%
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